Abstract.
The application of a statistical method, the local polynomial regression method, (LPRM), based on a nonparametric estimation of the regression function to determine the critical micelle concentration (cmc) is presented. The method is extremely flexible because it does not impose any parametric model on the subjacent structure of the data but rather allows the data to speak for themselves. Good concordance of cmc values with those obtained by other methods was found for systems in which the variation of a measured physical property with concentration showed an abrupt change. When this variation was slow, discrepancies between the values obtained by LPRM and others methods were found.
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References
R.J. Hunter, Foundations of Colloidal Science (Oxford University Press, Oxford 2001)
M.L. Corrin, J. Colloid Sci. 3, 333 (1948)
R.J. Williams, J.N. Phillips, K.J. Mysels, Trans. Faraday Soc. 51, 728 (1955)
J.N. Phillips, Trans. Faraday Soc. 51, 561 (1955)
D.G. Hall, B.A. Pethica, Nonionic Surfactants (Schick, M.J. Ed, Dekker, New York, 1967)
J.N. Israelachvili, D.J. Mitchell, B.W. Ninham, J. Chem. Soc., Faraday Trans. II 72, 1525 (1967)
M. Pérez-Rodríguez, G. Prieto, C. Rega, L.M. Varela, F. Sarmiento, V. Mosquera, Langmuir 14, 4422 (1998)
G.F. Simmons, J.S. Robertson, Differential Equations with Applications and Historical Notes (McGraw-Hill, New York, 1991)
P.R. Bevington, Data reduction and error analysis for the physical sciences (McGraw-Hill, New York, 1969)
J.M. Ruso, P. Taboada, D. Attwood, V. Mosquera, F. Sarmiento, Phys. Chem. Chem. Phys. 2, 1261 (2000)
J.M. Ruso, F. Sarmiento, Colloid Polym. Sci. 278, 800 (2000)
L. Besada, P. Martínez-Landeira, L. Seoane, G. Prieto, F. Sarmiento, J.M. Ruso, Mol. Phys. 24, 2003 (2001)
N.R. Draper, H. Smith, Applied regression analysis (Wiley-Interscience, New York, 1998)
H.-G. Müller, Nonparametric regression analysis of longitudinal data (Springer-Verlag, Berlin, 1988)
M. Francisco Fernández, La regresión polinómica local en diseño fijo con observaciones dependientes, Doctoral Thesis (Universidad de Santiago de Compostela, 2001)
J. Fan, I. Gijbels, Local polynomial modelling and its applications (Chapman and Hall, New York, 1996)
E.A. Nadaraya, Theory Probab. Appl. 15, 134 (1964)
G.S. Watson, Sankhya Ser. A 26, 359 (1964)
R.R. Macauley, The smoothing of time series (National Bureau of Economic Research, New York, 1931)
J. Fan, I. Gijbels, T.-C. Hu, L.-S. Huang, Statistica Sinica 6, 113 (1996)
B.W. Silverman, Density estimation for statistics and data analysis (Chapman and Hall, New York, 1986)
J.M. Ruso, D. Attwood, P. Taboada, M.J. Suarez, F. Sarmiento, V. Mosquera, J. Chem. Eng. Data 44, 941 (1999)
A. González-Pérez, J.L. del Castillo, J. Czapkiewicz, J.R. Rodríguez, J. Chem. Eng. Data 46, 709 (2001)
S. Causi, R. de Lisi, S. Milioto, J. Sol. Chem. 20, 1031 (1991)
E.M. Woolley, M.T. Bashford, D.G. Leaist, J. Sol. Chem. 31, 607 (2002)
S. Causi, R. de Lisi, S. Milioto, N. Tirone, J. Phys. Chem. 95, 5664 (1991)
E. Caponetti, S. Causi, R. de Lisi, M.A. Floriano, S. Milioto, R. Triolo, J. Phys. Chem. 96, 4950 (1992)
P. Taboada, D. Attwood, J.M. Ruso, M.J. Suarez, F. Sarmiento, V. Mosquera, J. Chem. Eng. Data 44, 820 (1999)
A. Siderius, S.K. Kehl, D.G. Leaist, J. Sol. Chem. 31, 607 (2002)
M.J. Suárez, J.L. López-Fontán, V. Mosquera, F. Sarmiento, J. Chem. Eng. Data 44, 1192 (1999)
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Received: 2 October 2003, Published online: 25 March 2004
PACS:
02.50.-r Probability theory, stochastic processes, and statistics - 82.70.-y Disperse systems; complex fluids
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López Fontán, J.L., Costa, J., Ruso, J.M. et al. A nonparametric approach to calculate critical micelle concentrations: the local polynomial regression method. Eur. Phys. J. E 13, 133–140 (2004). https://doi.org/10.1140/epje/e2004-00050-3
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DOI: https://doi.org/10.1140/epje/e2004-00050-3